Project #49747 - Statistics/Probability

Probability

 

Problem Set #2

 

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

Find the probability that the return for common stocks will be greater than 16.32%.

Find the probability that the return for common stocks will be greater than 5.89%.

Find the probability that the return for common stocks will be less than 14.37%.

Hint: There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site:

http://www.statsoft.com/textbook/sttable.html

 

Confidence Interval Estimation

2. Compute a 95% confidence interval for the population mean, based on the sample 1.5, 1.54, 1.55, 1.51, 0.09, 0.08, 1.55, 0.07, 0.99, 0.98, 1.12, 1.13, 1.00, 1.56, and 1.53. Change the last number from 1.53 to 50 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

 

Hypothesis Testing

3. The management of the Ceebler Fairy Corporation is considering relocating the corporate office to a new location outside HisWood Forest. Management is concerned that the commute times of the employees to the new office might be too long.
The company decides to survey a sample of employees at other companies in the same office forest to see how long these employees are commuting to the office. A sample of 23 employees indicated that the employees are commuting X (bar) = 33 minutes and s = 1 minute, 45 seconds.

a. Using the 0.01 level of significance, is there evidence that the population mean is above 32minutes?


b. What is your answer in (a) if X (bar) = 37 minutes and s = 27 minutes?


c. Look at your answers for a and b above and discuss what you can learn from the results about the effect of a large standard deviation.

 

4. Peter’s NEW IT Help company is concerned that the mean wait time of their phone customers for a customer service agent is not greater than 15 minutes. It can be assumed that the population variance is 9 minutes 6 seconds based on past experience. A sample of 563 customers is selected and the sample mean is 16 minutes 30 seconds. Using a level of significance of .10, is there evidence that the population mean wait time is greater than 15 minutes? Fully explain your answer.

 

 

Problem Set #3

Hypothesis Testing 
 

1.  University College is concerned that out of state students may be receiving lower grades than Maryland students. Two independent random samples have been selected: 165 observations from population 1 (Out of state students) and 177from population 2 (Maryland students). The sample means obtained are X1(bar)=86 and X2(bar)=87. It is known from previous studies that the population variances are 8.1 and 7.3 respectively. Using a level of significance of .01, is there evidence that the out of state students may be receiving lower grades? Fully explain your answer. 
 

Simple Regression

2.  A CEO of a large pharmaceutical company would like to determine if the company should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.

The use of linear regression is a critical tool for a manager's decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows: 
  
 

Month

Advertising Cost

Number of Orders

1

$74,430.00

2,856,000

2

62,620

1,800,000

3

67,580

1,299,000

4

53,680

1,510,000

5

69,180

1,367,000

6

73,140

2,611,000

7

85,370

3,788,000

8

76,880

2,935,000

9

66,990

1,955,000

10

77,230

3,634,000

11

61,380

1,598,000

12

62,750

1,867,000

13

63,270

1,899,000

14

86,190

3,245,000

15

60,030

1,934,000

16

79,210

2,761,000

17

67,770

1,625,000

18

84,530

3,778,000

19

79,760

2,979,000

20

84,640

3,814,000

 a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure.

NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. It should take about a minute.

b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysis to construct this equation.

c. Interpret the meaning of the slope, b1, in the regression equation.

d. Predict the monthly advertising cost when the number of orders is 2,300,000. (Hint: Be very careful with assigning the dependent variable for this problem)

e. Compute the coefficient of determination, r2, and interpret its meaning.

f. Compute the standard error of estimate, and interpret its meaning.

g. Do you think that the company should use these results from the regression to base any corporate decisions on?….explain fully.
 

Hypothesis Testing on Multiple Populations

3. Dr. Michaella Evans, a statistics professor at the University of Maryland University College, drives from her home to the school every weekday. She has three options to drive there. She can take the Beltway, or she can take a main highway with some traffic lights, or she can take the back road, which has no traffic lights but is a longer distance. Being as data-oriented as she is, she is interested to know if there is a difference in the time it takes to drive each route.

As an experiment she randomly selected the route on 21 different days and wrote down the time it took her for the round trip, getting to work in the morning and back home in the evening.  At the .01 significance level, can she conclude that there is a difference between the driving times using the different routes?

Time (in minutes) it took to get to work and back using:


 

Beltway

Main highway

Back road

88

79

86

94

86

78

91

75

79

88

83

96

98

74

97

84

72

73

90

 

68

77

   

You can check your critical value with the following table: HYPERLINK 

Subject Mathematics
Due By (Pacific Time) 12/02/2014 09:00 pm
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